Correlation energies of inhomogeneous many-electron systems

We generalize the uniform-gas correlation energy formalism of Singwi, Tosi, Land and Sjolander to the case of an arbitrary inhomogeneous many-particle system. For jellium slabs of finite thickness with a self-consistent LDA groundstate Kohn-Sham potential as input, our numerical results for the correlation energy agree well with diffusion Monte Carlo results. For a helium atom we also obtain a good correlation energy.Comment: 4 pages,1 figur

Effective action and density functional theory

The effective action for the charge density and the photon field is proposed as a generalization of the density functional. A simple definition is given for the density functional, as the functional Legendre transform of the generator functional of connected Green functions for the density and the photon field, offering systematic approximation schemes. The leading order of the perturbation expansion reproduces the Hartree-Fock equation. A renormalization group motivated method is introduced to turn on the Coulomb interaction gradually and to find corrections to the Hartree-Fock and the Kohn-Sham schemes.Comment: New references and a numerical algorithm added, to appear in Phys. Rev. B. 30 pages, no figure

Black Thunder Coal Mine and Los Alamos National Laboratory experimental study of seismic energy generated by large scale mine blasting

In an attempt to better understand the impact that large mining shots will have on verifying compliance with the international, worldwide, Comprehensive Test Ban Treaty (CTBT, no nuclear explosion tests), a series of seismic and videographic experiments has been conducted during the past two years at the Black Thunder Coal Mine. Personnel from the mine and Los Alamos National Laboratory have cooperated closely to design and perform experiments to produce results with mutual benefit to both organizations. This paper summarizes the activities, highlighting the unique results of each. Topics which were covered in these experiments include: (1) synthesis of seismic, videographic, acoustic, and computer modeling data to improve understanding of shot performance and phenomenology; (2) development of computer generated visualizations of observed blasting techniques; (3) documentation of azimuthal variations in radiation of seismic energy from overburden casting shots; (4) identification of, as yet unexplained, out of sequence, simultaneous detonation in some shots using seismic and videographic techniques; (5) comparison of local (0.1 to 15 kilometer range) and regional (100 to 2,000 kilometer range) seismic measurements leading to determine of the relationship between local and regional seismic amplitude to explosive yield for overburden cast, coal bulking and single fired explosions; and (6) determination of the types of mining shots triggering the prototype International Monitoring System for the CTBT

Conformal Field Theory and Hyperbolic Geometry

We examine the correspondence between the conformal field theory of boundary operators and two-dimensional hyperbolic geometry. By consideration of domain boundaries in two-dimensional critical systems, and the invariance of the hyperbolic length, we motivate a reformulation of the basic equation of conformal covariance. The scale factors gain a new, physical interpretation. We exhibit a fully factored form for the three-point function. A doubly-infinite discrete series of central charges with limit c=-2 is discovered. A correspondence between the anomalous dimension and the angle of certain hyperbolic figures emerges. Note: email after 12/19: [email protected]: 7 pages (PlainTeX

Enhanced Fusion-Evaporation Cross Sections in Neutron-Rich 132^{132}Sn on 64^{64}Ni

Evaporation residue cross sections have been measured with neutron-rich radioactive $^{132}$Sn beams on $^{64}$Ni in the vicinity of the Coulomb barrier. The average beam intensity was $2\times 10^{4}$ particles per second and the smallest cross section measured was less than 5 mb. Large subbarrier fusion enhancement was observed. Coupled-channels calculations taking into account inelastic excitation and neutron transfer underpredict the measured cross sections below the barrier.Comment: 4 pages including 1 table and 3 figure

Metal Surface Energy: Persistent Cancellation of Short-Range Correlation Effects beyond the Random-Phase Approximation

The role that non-local short-range correlation plays at metal surfaces is investigated by analyzing the correlation surface energy into contributions from dynamical density fluctuations of various two-dimensional wave vectors. Although short-range correlation is known to yield considerable correction to the ground-state energy of both uniform and non-uniform systems, short-range correlation effects on intermediate and short-wavelength contributions to the surface formation energy are found to compensate one another. As a result, our calculated surface energies, which are based on a non-local exchange-correlation kernel that provides accurate total energies of a uniform electron gas, are found to be very close to those obtained in the random-phase approximation and support the conclusion that the error introduced by the local-density approximation is small.Comment: 5 pages, 1 figure, to appear in Phys. Rev.

Self-dual noncommutative \phi^4-theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory

We study quartic matrix models with partition function Z[E,J]=\int dM \exp(trace(JM-EM^2-(\lambda/4)M^4)). The integral is over the space of Hermitean NxN-matrices, the external matrix E encodes the dynamics, \lambda>0 is a scalar coupling constant and the matrix J is used to generate correlation functions. For E not a multiple of the identity matrix, we prove a universal algebraic recursion formula which gives all higher correlation functions in terms of the 2-point function and the distinct eigenvalues of E. The 2-point function itself satisfies a closed non-linear equation which must be solved case by case for given E. These results imply that if the 2-point function of a quartic matrix model is renormalisable by mass and wavefunction renormalisation, then the entire model is renormalisable and has vanishing \beta-function. As main application we prove that Euclidean \phi^4-quantum field theory on four-dimensional Moyal space with harmonic propagation, taken at its self-duality point and in the infinite volume limit, is exactly solvable and non-trivial. This model is a quartic matrix model, where E has for N->\infty the same spectrum as the Laplace operator in 4 dimensions. Using the theory of singular integral equations of Carleman type we compute (for N->\infty and after renormalisation of E,\lambda) the free energy density (1/volume)\log(Z[E,J]/Z[E,0]) exactly in terms of the solution of a non-linear integral equation. Existence of a solution is proved via the Schauder fixed point theorem. The derivation of the non-linear integral equation relies on an assumption which we verified numerically for coupling constants 0<\lambda\leq (1/\pi).Comment: LaTeX, 64 pages, xypic figures. v4: We prove that recursion formulae and vanishing of \beta-function hold for general quartic matrix models. v3: We add the existence proof for a solution of the non-linear integral equation. A rescaling of matrix indices was necessary. v2: We provide Schwinger-Dyson equations for all correlation functions and prove an algebraic recursion formula for their solutio

Large deviation techniques applied to systems with long-range interactions

We discuss a method to solve models with long-range interactions in the microcanonical and canonical ensemble. The method closely follows the one introduced by Ellis, Physica D 133, 106 (1999), which uses large deviation techniques. We show how it can be adapted to obtain the solution of a large class of simple models, which can show ensemble inequivalence. The model Hamiltonian can have both discrete (Ising, Potts) and continuous (HMF, Free Electron Laser) state variables. This latter extension gives access to the comparison with dynamics and to the study of non-equilibri um effects. We treat both infinite range and slowly decreasing interactions and, in particular, we present the solution of the alpha-Ising model in one-dimension with $0\leq\alpha<1$

On the Relationship between Yang-Mills Theory and Gravity and its Implication for Ultraviolet Divergences

String theory implies that field theories containing gravity are in a certain sense `products' of gauge theories. We make this product structure explicit up to two loops for the relatively simple case of N=8 supergravity four-point amplitudes, demonstrating that they are `squares' of N=4 super-Yang-Mills amplitudes. This is accomplished by obtaining an explicit expression for the $D$-dimensional two-loop contribution to the four-particle S-matrix for N=8 supergravity, which we compare to the corresponding N=4 Yang-Mills result. From these expressions we also obtain the two-loop ultraviolet divergences in dimensions D=7 through D=11. The analysis relies on the unitarity cuts of the two theories, many of which can be recycled from a one-loop computation. The two-particle cuts, which may be iterated to all loop orders, suggest that squaring relations between the two theories exist at any loop order. The loop-momentum power-counting implied by our two-particle cut analysis indicates that in four dimensions the first four-point divergence in N=8 supergravity should appear at five loops, contrary to the earlier expectation, based on superspace arguments, of a three-loop counterterm.Comment: Latex, 52 pages, discussion of 2 loop divergences in D=8,10 adde